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# Calculation of Rope Drum for Overhead Cranes

## ## Introduction

Calculation Online : When it comes to the performance of wire rope in a machine, the design of its sheaves and drums plays a crucial role. In this article, we will explore the important factors to consider when designing sheaves and drums for wire ropes used in overhead cranes. We will also discuss various technical aspects of wire ropes, such as measurement of diameter, design factors, capacity of drums and reels, reserve strength, wire rope clips, and wire rope end connections.

## Sheave and Drum Design

The design of sheaves and drums greatly impacts the life and performance of a wire rope. Two key factors to consider in the design are sheave and drum diameters. The D/d ratio, where D is the sheave or drum diameter and d is the wire rope diameter, determines the reduction in rope strength when it passes over a curved surface. Smaller D/d ratios result in a greater loss of strength.

To ensure the optimal design of sheaves and drums, relevant standard or statutory requirements should be followed. In the absence of such requirements, the minimum diameter of the drum or sheave should not be less than the values specified for different purposes and constructions.

Sheave and Drum Design

## Groove Dimensions

The groove dimensions of sheaves and drums are crucial for ensuring the proper functioning and longevity of wire ropes. The radius of the groove should be slightly larger than that of the rope passing over it. A too narrow groove can crush the rope and damage the wires, while a too wide groove can cause wear and cut a false groove in the pulley.

For sheaves, the recommended dimensions for the groove radius, depth, and throat angles are as follows:

• Groove radius (r): Minimum = 0.53 to 0.535 x d and Maximum = 0.55 x d
• Groove depth (h): 1.5 x d
• Throat angle: 35° to 45° (for normal applications)

For drums, the recommended dimensions for the groove radius, depth, and pitch are as follows:

• Groove radius (r): Minimum = 0.53 to 0.535 x d and Maximum = 0.55 x d
• Groove depth (h): Minimum h ≥ 0.374 x d for helically grooved drums
• Pitch (p): The pitch shall not be smaller than 2.065 x groove radius and larger than 2.18 x groove radius

## Sheave and Drum Design as per IS 3177

IS 3177 is a code of practice for electric overhead traveling cranes and gantry cranes. The design of sheaves and drums for these cranes depends on the mechanism class, which is determined by different duty factors and average life.

The D/d ratio for drums and sheaves varies based on the rope construction and mechanism class. For example, the D/d ratio for 6×19 group multi-strand ropes is 17 to 22 for mechanism class 6×19.

The diameter of the groove in drums and sheaves depends on the rope diameter. As per IS 3177, the increase over the rope radius ranges from 1.0 mm to 3.0 mm for different rope diameters.

## Fleet Angle

The fleet angle is the angle at which a wire rope deviates from alignment with the sheave when it leads over a sheave and onto a drum. The fleet angle depends on the width of the drum and the distance from the fixed sheave.

To ensure the correct fleet angle, a formula can be used to calculate the height of the lead pulley or the width of the drum. The formula is C = A/B, where C is a constant based on the type of drum (0.07 for flat-faced drums and 0.14 for grooved drums), A is the height of the lead pulley or the width of the drum, and B is the rope diameter.

As per IS 3177, the fleet angle should not exceed 5 degrees.

## Diameter of a Wire Rope

The diameter of a wire rope is the diameter of a circle circumscribing the strands. It is important to measure the rope diameter correctly, as it can vary from the nominal diameter of the rope. The actual diameter usually varies from -1% to 4% of the nominal diameter, as per IS 2266.

When measuring the rope diameter, it is advisable to measure the rope when it is straight and not on the reel. The correct diameter should be measured at a point in the rope by placing the calipers over each pair of opposite strands and averaging the readings.

## Generally Accepted Design Factors

Different purposes and types of services require different design factors for wire ropes. These design factors ensure the safe and reliable operation of wire ropes in various applications.

For fixed guys, derricks, jib cranes, etc., a minimum design factor of 4.0 is generally accepted. For general engineering, slings, and hot ladle cranes, the minimum design factors are 5.0 and 8.0, respectively.

The design factors also vary based on the rope speed and type of lift. For passengers and goods lifts and hoists, the design factors range from 10.0 to 12.0, depending on the rope speed.

## Capacity of Drums and Reels

The capacity of a drum or reel is a crucial consideration when determining how much wire rope it can hold. The capacity is calculated using the formula (A+B) x A x C x K, where A is the depth of the rope space, B is the drum diameter, C is the width of the drum between flanges, and K is a constant based on the rope diameter.

The constant K varies based on the rope diameter and is specified in a table. The capacity can be calculated in feet or meters, depending on the unit used for the constant.

## Reserve Strength

The reserve strength of a wire rope refers to the strength of the rope exclusive of the outer layer of wires that may be damaged. The reserve strength is expressed as a percentage of the total strength of a well-lubricated new rope.

The reserve strength varies based on the construction of the wire rope. For example, for a 6×19 group wire rope with a steel core, the reserve strength of the outer wires is 74% and the inner wires is 52% of the total strength.

## Wire Rope Clips

Wire rope clips, also known as bulldog clips, are a mechanical means of securing a wire rope around a thimble. They serve as an alternative to splicing and are made from malleable iron or drop-forged steel.

Malleable wire rope clips are suitable for non-critical, light-duty applications with small applied loads. They should not be used for lifting or suspending loads. The efficiency of wire rope clips depends on the rope size and core type.

## Wire Rope End Connections

Various types of end connections are used for overhead lifting applications. These connections provide a secure attachment point for wire ropes and have different efficiency ratings based on the difference between the actual breaking strength of the rope and the attained breaking strength with a specific fitting.

Spelter sockets are the only fitting that can attain 100% efficiency if properly attached. Other end connections, such as swaged fittings, may have a slight loss of rope strength due to the compression of the rope during the swaging process.

## Conclusion

Designing sheaves and drums for wire ropes used in overhead cranes requires careful consideration of various factors, including sheave and drum diameters, groove dimensions, fleet angle, rope diameter, design factors, capacity of drums and reels, reserve strength, wire rope clips, and wire rope end connections. By following the relevant standards and guidelines, engineers can ensure the safe and efficient operation of wire ropes in overhead crane applications.

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